Question: Rewrite the expression in the form $k\cdot x^n$. $2\sqrt x\cdot 4x{^{^{-\scriptsize\dfrac52}}}=$
Solution: $\begin{aligned} 2\sqrt x\cdot 4x^{^{\scriptsize-\dfrac52}}&=2x^{^{\scriptsize\dfrac12}}\cdot 4x^{^{\scriptsize-\dfrac52}} \\\\ &=2\cdot4\cdot x^{^{\scriptsize\dfrac12-\dfrac52}} \\\\ &=8x^{-2} \end{aligned}$